We introduce a generalized dual decomposition bound for computing the maximum expected utility of influence diagrams based on the dual decomposition method generalized to $L^p$ space. The main goal is to devise an approximation scheme free from translations required by existing variational approaches while exploiting the local structure of sum of utility functions as well as the conditional independence of probability functions. In this work, the generalized dual decomposition method is applied to the algebraic framework called valuation algebra for influence diagrams which handles probability and expected utility as a pair. The proposed approach allows a sequential decision problem to be decomposed as a collection of sub-decision problems of bounded complexity and the upper bound of maximum expected utility to be computed by combining the local expected utilities. Thus, it has a flexible control of space and time complexity for computing the bound. In addition, the upper bounds can be further minimized by reparameterizing the utility functions. Since the global objective function for the minimization is nonconvex, we present a gradient-based local search algorithm in which the outer loop controls the randomization of the initial configurations and the inner loop tightens the upper-bound based on block coordinate descent with gradients perturbed by a random noise. The experimental evaluation demonstrates highlights of the proposed approach on finite horizon MDP/POMDP instances.
A typical example of this approach is expressing knowledge by rules. The underlying assumption is that these representations are compact abstractions of the known individual instances of the knowledge concept to be encoded. These abstractions can be static or dynamic, i.e., they can be compiled into the program directly, or adaptively synthesized during the application execution with a learning procedure. This approach is applicable for representing well-organized knowledge. However, such a summarization approach has faced substantial problems in applications where the concepts required for the knowledge are highly interconnected and have a large amount of irregularities (exceptions), e.g., "common sense".
This paper compares various optimization methods for fuzzy inference system optimization. The optimization methods compared are genetic algorithm, particle swarm optimization and simulated annealing. When these techniques were implemented it was observed that the performance of each technique within the fuzzy inference system classification was context dependent.
Bayesian methods of matrix factorization (MF) have been actively explored recently as promising alternatives to classical singular value decomposition. In this paper, we show that, despite the fact that the optimization problem is non-convex, the global optimal solution of variational Bayesian (VB) MF can be computed analytically by solving a quartic equation. This is highly advantageous over a popular VBMF algorithm based on iterated conditional modes since it can only find a local optimal solution after iterations. We further show that the global optimal solution of empirical VBMF (hyperparameters are also learned from data) can also be analytically computed. We illustrate the usefulness of our results through experiments.